So perhaps I’ll be coming to the end of posts on the subject of unusual weather for a while. Until there’s some more!

We’ve seen that March 2013 was, with 1892, the equal coldest in the CET since 1883, which is particularly significant given the generally warmer Marches in recent decades.

The first quarter of 2013 was the coldest since 1987, and the cold has now continued into April. This is where we now are, according to the Met Office:

So far this year it’s been 1.44C colder than the average over 1961-90, which is the basis for CET “anomalies” here.

The rest of the year would have to be 2.37C warmer than usual, on average, for 2013 to be the warmest in the record.

Is it possible for 2013 to still be the warmest year in the CET? I’m saying no – or, to be more measured, it’s extremely unlikely.

Last year, it was July 13th before I felt able to make a similar statement.

But now I’ve realised that I can simply plot a graph of the later parts of previous years and compare them to the required mean temperature in 2013.

Here’s the graph of mean CET for the last 9 months of the year:

Perhaps the most notable feature is that the last 9 months of 2006, at 13C were a whole 0.5C warmer than the last 9 months of the next warmest year, 1959, at 12.5C!

It’s easy enough to calculate that for 2013 to be the warmest year in the CET, the mean temperature for the last 9 months of the year would have to be 13.38C.

To be warmer than the warmest year in the CET, also 2006, the last 9 months of 2013 would need to be 0.38C warmer than the last 9 months of 2006. That’s a big ask.

But let’s look a little more carefully at 1959. The last 9 months of 2009 were about 1.4C warmer than the prevailing mean temperatures at the time, given by the 11 year (red line) and 21 year (black line) running means. The last 9 months of 2006 were “only” about 1.1 or 1.2C warmer than an average year at that time.

If 2013 were 1.4C warmer than the running means in previous years (obviously we can only determine the running means centred on 2013 with hindsight) then it would not be far off the warmest year in the CET.

No other year in the entire CET spikes above the average as much as 1959, so we have to suppose the last 9 months of that year were “freak” – say a once in 400 year event – and extremely unlikely to be repeated.

So on this basis it seems 2013 is extremely unlikely to be the warmest in the CET.

Now we have a bit of data for April we can also carry out a similar exercise for the last 8 months of the year.

The Met Office notes (see the screen-grab, above) that the first 8 days of April 2013 were on average 3C cooler than normal in the CET (“normal” with respect to the CET is always the 1961-90 average). If we call those 8 days a quarter of the month, the rest of the month needs to be 1C warmer than usual for April as a whole to be average. Let’s be conservative, though, and assumes that happens.

It’s easy enough now to calculate that for 2013 to be the warmest year in the CET, the mean temperature for the last 8 months of the year would have to be 14.07C, assuming the April temperature ends up as the 1961-90 average.

On this basis, we can then compare the last 8 months of previous years in the CET with what’s required for this year to be the warmest on record:

Here 2006 seems more exceptional, and 1959 not quite such an outlier. (April is not now included: in 1959 the month was warm at 9.4C whereas in 2006 it was warmer than average at 8.6C, but not unusual).

Clearly, the spike above the running means would have to be a lot higher than ever before for 2013 to be the warmest year in the CET. Those 8 cold days seem to have made all the difference to the likelihood of 2013 breaking the record.

That’s it for now – though if April is particularly cold this year, a comparison of March and April with those months in previous years will be in order. The plot-spoiler is that 1917 was the standout year in the 20th century for the two months combined.

The CET record goes back to 1659, so the historical significance of an exceptionally cold or warm spell – a month, season, year or longer – can be judged over a reasonably long period. Long-term trends, such as the gradual, irregular warming that has occurred since the late 17th century, are, of course, also readily apparent. The Met Office bases press releases and suchlike on records for the UK as a whole which go back only to 1910.

The Met Office update the CET for the current month on a daily basis, which is very handy for seeing how things are going.

After watching the CET carefully during a few extreme months – December 2010 and March 2013 come to mind – I noticed that there seems to be a downwards adjustment at the end of the month. I speculated about the reasons for the apparent correction to the figures a week or so ago:

“…I’ve noticed the CET is sometimes adjusted downwards before the final figure for the month is published, a few days into the next month. I don’t know why this is. Maybe the data for more remote (and colder) weather-stations is slow to come in. Or maybe it’s to counter for the urban heat island effect, to ensure figures are calibrated over the entire duration of the CET.”

and, as I mentioned earlier, today emailed the Met Office to ask.

I received a very prompt reply, and the first of the possible explanations I came up with is in fact correct. My phrase “more remote” makes it sound like the data is still being collected by 18th century vicars and landed gentry, but in fact there is a bias in the daily CET for the month to date due to the timing of availability of data:

“Not all weather stations send us their reports in real time, i.e. every day, and so for some stations we have to wait until after the end of the month before [complete] data are available.”

It must simply be that the stations that send in the data later tend to be in colder areas (at least in winter when I’ve noticed the end of month adjustment) – perhaps they really are “more remote”!

Well, it did it!

Here’s a list of the coldest Marches since 1800 in the CET:

1.   1883  1.9C
2.   1845  2.0C
3.   1837  2.3C
4= 1892  2.7C
4= 2013  2.7C
5.   1962  2.8C

A few questions and not quite so many answers occur to me:

1. Why hasn’t the Met Office trumpeted March 2013 as the coldest since the 19th century?
What I’m alluding to here is, first, that the Met Office records for the UK and England only go back to 1910, but also that, as detailed on the Met Office’s blog, it turns out that March 2013 was only the joint 2nd coldest for the UK as a whole:

“March – top five coldest in the UK
1 1962 1.9 °C
2 2013 2.2 °C
2 1947 2.2 °C
4 1937 2.4 °C
5 1916 2.5 °C”

and second coldest for England as a whole:

“Looking at individual countries, the mean temperature for England for March was 2.6 °C – making it the second coldest on record, with only 1962 being colder (2.3 °C). In Wales, the mean temperature was 2.4 °C which also ranks it as the second coldest recorded – with only 1962 registering a lower temperature (2.1 °C). Scotland saw a mean temperature of 1.3 °C, which is joint fifth alongside 1916 and 1958. The coldest March on record for Scotland was set in 1947 (0.2 °C). For Northern Ireland, this March saw a mean temperature of 2.8 °C, which is joint second alongside 1919, 1937, and 1962. The record was set in 1947 (2.5 °C).”

The figures all tally suggesting that the parts of England not included in the CET were less exceptionally cold than those included, as I suggested before.

2. Why hasn’t the Met Office trumpeted March 2013 as the second coldest on record?
What I’m alluding to here is that the Met Office only made their “second coldest” announcement on their blog, not with a press release. The press release they did issue on 26th March was merely for “the coldest March since 1962″, and included somewhat different data to that (above) which appeared on their blog for the whole month:

“This March is set to be the coldest since 1962 in the UK in the national record dating back to 1910, according to provisional Met Office statistic [sic].

From 1 to 26 March the UK mean temperature was 2.5 °C, which is three degrees below the long term average. This also makes it joint 4th coldest on record in the UK.

Looking at individual countries, March 2013 is likely to be the 4th coldest on record for England, joint third coldest for Wales, joint 8th coldest for Scotland and 6th coldest for Northern Ireland.” (my stress)

and a “top 5″ ranking that doesn’t even include March 2013, which eventually leapt into 2nd place!:

“March – Top five coldest in the UK
1 1962 1.9 °C
2 1947 2.2 °C
3 1937 2.4 °C
4 1916 2.5 °C
5 1917 2.5 °C.”

As I’ve also mentioned before, it’s odd to say the least that the Met Office have formally released provisional data (and not the actual data!) to the media.

So I’ve asked them why they do this, by way of a comment on their blog:

“The Met Office’s [sic - oops] announced a few days ago that March 2013 was only the ‘joint 4th coldest on record’ (i.e. since 1910) rather than the joint 2nd coldest. This was based on a comparison of data to 26th in 2013 with the whole month in earlier years, which seems to me a tad unscientific.

Maybe it’s just me, but it seems that there was more media coverage of the earlier, misleading, announcement.

Why did the Met Office make its early announcement and not wait until complete data became available at the end of the month?”

I’ll let you know when I receive a response – my comment has been awaiting moderation for 4 days now.

3. Why was it not clearer from the daily CET updates that March 2013 would be as cold as 2.7C?
And what I’m alluding to here is the end of month adjustment that seems to occur in the daily updated monthly mean CET data. I’ve noticed this and so has the commenter on my blog, “John Smith”.

I didn’t make a record of the daily mean CET for March to date, unfortunately, but having made predictions of the final mean temperature for March 2013 on this blog, I checked progress. From memory the mean ticked down to 2.9C up to and including the 30th, but was 2.7C for the whole month, i.e. after one more day. At that stage in the month, it didn’t seem to me possible for the mean CET for the month as a whole to drop more than 0.1C in a day (and it had been falling by less, i.e. by 0.1C less often than every day). Anyway, I’ve emailed the Met Office CET guy to ask about the adjustment. Watch this space.

4. Does all this matter?
Yes, I think it does.

Here’s the graph for March mean CET I produced for the previous post, updated with 2.7C for March 2013:

A curiosity is that never before has a March been so much colder – more than 5C – than the one the previous year. But the main point to note is the one I pointed out last time, that March 2013 has been colder than recent Marches – as indicated by the 3 running means I’ve provided – by more than has occurred before (except after the Laki eruption in 1773).

I stress the difference with recent Marches rather than just March 2012, because what matters most in many areas is what we’re used to. For example, farmers will gradually adjust the varieties of crops and breeds of livestock to the prevailing conditions. A March equaling the severity of the worst in earlier periods, when the average was lower, will then be more exceptional and destructive in its effects.

The same applies to the natural world and to other aspects of the human world. For example, species that have spread north over the period of warmer springs will not be adapted to this year’s conditions.  And we gradually adjust energy provision – such as gas storage – on the basis of what we expect based on recent experience, not possible theoretical extremes.

OK, this has just been a cold March, but it seems to me we’re ill-prepared for an exceptional entire winter, like 1962-3 or 1740. And it seems such events have more to do with weather-patterns than with the global mean temperature, so are not ruled out by global warming.

Overall, though, the Met Office analysis – which, remember, is based on a series going back only to 1910 – suggests 2013 has been less of an outlier than it is in the Central England Temperature (CET) record.

This is what they say:

“This March is set to be the coldest since 1962 in the UK in the national record dating back to 1910, according to provisional Met Office statistic.

From 1 to 26 March the UK mean temperature was 2.5 °C, which is three degrees below the long term average. This also makes it joint 4th coldest on record in the UK.”

They provide a list:

“March – Top five coldest in the UK

1 1962 1.9 °C
2 1947 2.2 °C
3 1937 2.4 °C
4 1916 2.5 °C
5 1917 2.5 °C”

The discrepancy with the CET is presumably partly because Scotland, although colder than England, has not been as extreme compared to the cold Marches of the 20th century. The Met Office note:

“Looking at individual countries, March 2013 is likely to be the 4th coldest on record for England, joint third coldest for Wales, joint 8th coldest for Scotland and 6th coldest for Northern Ireland.”

Still, I’m rather puzzled why this March is reported as only the 4th coldest in England, particularly when I read in a post the Met Office’s blog that in most English counties it’s been the 2nd coldest after 1962.

It may be that the overall ranking for England will change over the next few days, which would add to my bafflement as to why the Met office makes early announcements. I’d have thought such behaviour was fine for mere bloggers like me, but not what is expected from an authoritative source. Isn’t the difference the same as that between City company analysts and the companies themselves? The former speculate; the latter announce definitive results.

Anyway, it’s also possible that the CET region has been colder than England as a whole relative to the previous cold Marches. I notice on the Met Office blog that this March has not been the second coldest for Yorkshire, Northumberland and Durham. If these are outside the CET area, their significant area would explain the difference in the Met Office rankings for England as a whole.

Focusing just on the CET, it’s still possible that March 2013 could be as cold or colder than 1962, and therefore the equal coldest since 1892 or 1883 (or even the coldest since 1883, though that seems unlikely now).

Although daily maximum temperatures have increased slightly to 6C or so, we’re also expecting some serious frosts (in fact some daily minimum records look vulnerable on 30th and 31st), and the CET website implies it is a (min+max)/2 statistic (as included in the screen-grab below).

Here’s the latest CET information for March:

It’s now very easy to work out what the mean temperature will be at the end of the March, due to the happy coincidence of the mean being 3.1 so far and there being 31 days in the month (regular readers will have noticed that I much prefer ready reckoning methods to those involving calculators or spreadsheets). Obviously, spread over the whole month the 3.1C so far would be 2.7C. That is, if the mean temperature for the remaining 4 days were 0C, that for the month would be 2.7C, the same as 1892 (and lower than 1962s 2.8C). Every 3.1 degree days above 0 (that is ~0.75C mean for the 4 days) adds 0.1C (over 2.7C) for the month as a whole. So if you think it’ll average 1.5C for the rest of the month in the CET region, the mean for the month as a whole will be 2.9C.

Obviously rounding could come into it, so it might be worth noting that the mean to 26th was also 3.1C. If you think (or find out – due to time constraints, I haven’t drilled down on the CET site) that 27th was colder than 3.1C (which seems likely) then just a bit less than 1.5C for the rest of the month – say 1.4C – would likely leave the overall mean at 2.8C.

Here’s the latest ensemble chart for London temperatures from the Weathercast site to help you make your mind up:

My guesstimate is 2.8C, so on that basis I move on to the main point of this post. Just for a bit of fun I put together a chart of the entire CET record for March, with running means:

The picture is not dissimilar to that for the unusually cool summer of 2011. Although this March has been the coldest for “only” 50 years – one might argue that a coldest for 50 years month will occur on average every 50 months, i.e. every 4 and a bit years – global and general UK (including CET) temperatures have increased significantly over the last few decades.

As can be seen from the chart above, this March has been around 3.5 degrees colder than the running mean (depending which you take).

I say this with the health warning (as I gave for summer 2011) that the running means may be dragged down if March is also cold over the next few years – the significance of extreme events can only be fully appreciated in hindsight, and it may be that the warm Marches of the two decades or so before this year will look more exceptional and this year’s less exceptional when we have the complete picture.

Health-warning aside, there aren’t really any other Marches as much as 3.5C colder than the prevailing March temperature. The period 1783-6 stands out on the graph, but isn’t really comparable, because the eruption of the Icelandic volcano Laki gave the country a sulphurous shade, significantly reducing the Sun’s warmth. 1674 looks notable, too, but the monthly means back then seem to be rounded to the nearest degree centigrade, so we can’t be sure it actually was as cold as 1C (at least without considerable further research).

It’s all very curious. After December 2010 (for which I should prepare a similar chart some time) and now March 2013, one wonders whether, when we do get cold snaps, it’s going to be even more of a shock than in the past. Does global warming have much less effect on cold UK winter temperatures than on the long-term average? Or would this March have been even colder had the same weather conditions occurred before the global warming era? March 1883 averaged 1.9C, but was only about 3C colder than prevailing Marches. Perhaps this year’s weather conditions would have resulted in a monthly mean of 1.4C back then! The trouble is we now have no idea whether this March has been a once in 50 years, once a century or once a millennium event.

And has melting the Arctic ice made cold snaps more likely?

Confusion and unpredictability abounds when it comes to extreme weather events. Preparing for the worst – the precautionary principle – is called for.

Besides, I’ve already prepared a chart. I’ve already noted that the meteorological winter 2012-13 (December, January and February) was no colder than 3 of the previous 4, although there has been an abrupt change from the milder winters seen since 1990-1, the winter of “the wrong kind of snow”.

Nor, as we also saw, has the “long winter” (December through March) 2012-13 been as cold as 2009-10.

But if we disregard December and instead take the “late winter”, or the first quarter of the calendar year, then 2013 is colder than 2010, in fact the coldest since 1987:

There are a few points to note from this graph:

1.The roll-call of Great Winters from the Dec-Feb and Dec-Mar graphs in previous posts is not affected too much.  1684 and 1740 are still the stand-outs.  1963 drops to 5th, with 1795 being a shade more notable than in the other analyses.

2. The abrupt change over the last few years, with two first quarters averaging well under 4C following over a decade of milder starts to the year.  The 5-year running mean (green line) is down 1.3C or so from its peak around the turn of the millennium.

3. The fact that the cold start to this year makes it very unlikely that 2013 will be the warmest in the CET – I’ll endeavour to make this the topic of another post.

4. The fact that even in this analysis there have been lots of winters colder than 2013.   Indeed, the 5 year running mean temperature for the first quarter is still higher than it’s been most of the time, even during the 20th century!  This year as a whole has so far been significantly milder than those in the period 1985-7 (when I seem to recollect spending a lot of time walking across frozen car-parks) and 1979, the Winter of Discontent, let alone 1963, 1947, 1917, 1895…  Perhaps that’s something that ought to be borne in mind by those whose responsibility it is to secure the UK’s gas and other energy supplies.  Despite the experience of the last few winters I suspect we’re still woefully under-prepared for what Nature could throw at us.

The nation-wide statistics published by the Met Office only go back to 1910, so the Central England Temperature (CET) record is needed to put current weather in a long-term context.

1892 is an odd year for the Daily Mail to choose, since the CET for March that year was 2.7C, whereas 1962, the year we have to “beat” for it to be the coldest since 1892, saw a mean March CET of 2.8C. We’re unlikely to say this March is “the coldest since 1883″, since if it comes in at 2.8C we’d probably say it’s the “equal coldest since 1892″ and if it comes in at 2.7C we might say it’s the “equal coldest since 1883″.

Furthermore, given the possibility of rounding, the difference between 1892 and 1962 could be much less than 0.1C, for all I know.

In addition, the difficulties of calibrating temperature readings between 1892 and 1962 make a difference of 0.1C in a monthly mean fairly insignificant (and probably statistically insignificant). To put it another way, the error bars on the temperatures are probably greater than 0.1C. Perhaps we shouldn’t really be quibbling over the difference between monthly means of 2.7C and 2.8C. But then again, we do like our weather records!

If this March is colder even than that in 1892, the next mark is 1883, when March saw a CET of 1.9C. It’s no longer on the cards for it to be as cold as 1.9C this March.

But what are the chances of the CET this March being colder than 2.8C or even 2.7C?

Here’s the state of play at the moment:

This is moreorless in line with my projection of a few days ago. But that was based on ensemble forecasts on 22nd March, and, as I noted yesterday, the forecast for the rest of March has just kept getting colder since 22nd:

Based on the forecast for 22nd March I wrote:

“Ignoring today (22nd) as transitional, it now looks likely that the 5 days 23rd through 27th March will be seriously cold, so let’s knock 0.1C off the monthly average for each of them. That gets us down to 3.1C.

The 28th will most likely be around the new average (3.1C), so it all depends on when the mild air comes in from the Atlantic. The computer model runs (grey lines) differ, and the average (yellow line) for 30th and 31st are for it to be relatively mild. If that’s the case, then we’d need to add on 0.1C for each day, so would roughly equal 1969.”

It’s certainly now not the case that 30th and 31st will be “relatively mild”, so we won’t have to add on 0.1C for each of those days. This March is therefore very likely to be colder than 1969 (3.3C) and therefore the coldest since at least 1962.

But could it be even colder than the 2.8C in 1962?

Here’s a larger image of the current ensemble forecast from the Weathercast site:

The CET mean for March so far is 3.2C. To depress this average the mean for the rest of March would have to be lower than 3.2C, obviously. And since there’s 31 days in the month, each degree it is lower than 3.2C over one day (what we might call a degree-day) will depress the monthly mean by 1/31st of a degree.

The ensemble chart suggests the mean temperature for London for the rest of March will be about 1.5C – your judgement is as good as mine – over 6 days, so that’s very roughly 12 degree days lower than 3.2C (about 2C each day), so dividing by 30 (rounding 31), we might expect the mean for the month to come out about 0.4C lower than it is now, at 2.8C.

This estimate is very rough and ready since I’ve assumed in particular that London is representative of the CET region. It’s quite possible the region as a whole will be colder than London. Not only might this be the case generally, but there’s a lot of lying snow in more northerly areas, which tends to depress temperature readings (because it resists warming by reflecting sunlight and because its latent heat buffers warming of the ground surface at about 0C, both preventing warming of the air above it, and it is the near-ground air temperature that’s being measured).

Additionally, I’ve noticed the CET is sometimes adjusted downwards before the final figure for the month is published, a few days into the next month. I don’t know why this is. Maybe the data for more remote (and colder) weather-stations is slow to come in. Or maybe it’s to counter for the urban heat island effect, to ensure figures are calibrated over the entire duration of the CET.

By way of a sanity-check, here’s another view of much the same ensemble data as in the previous image, from the Wetterzentrale site:

Note that to depress the average for the month so far the temperature would need to be around 4C less than usual, since the mean CET mean (!) for the whole of March is about 5.7C and it’s near the end of the month when mean daily temperatures around 7C would be typical. On that basis the Wetterzentrale maps suggest that 12 degree-days lower than the mean for the month so far is a reasonably estimate for the outlook over the next 6 days.

If a best guess is that the mean CET for March 2013 is 2.8C (“equal coldest since 1892″), with some uncertainty, it certainly seems possible that it could instead come in at 2.7C (“equal coldest since 1883″). In either case, though, it might be more accurate to simply say it has been one of the coldest 3 Marches since March 1883. I like to be fairly conservative, but I suppose there’s just an outside chance the mean CET this month could be even lower, at 2.6C, say, in which case we’d probably claim it has been the coldest since 1883.

Of course, this is all just estimation: the mean CET for March 2013 might end up “only” as cold as say 2.9C, the coldest for 51 years!

“Weather forecasting (and climate prediction) is not just about computer power. Deep philosophical ideas also come into play.”

I fear I may have under-delivered on the philosophy.

I intended to suggest that all forecasts, such as of weather, are necessarily and systematically inaccurate.

To recap, my main point yesterday was that running an inaccurate forecasting model numerous times doesn’t solve all the inherent problems:

“All ensemble forecasters know is that a certain proportion of computer model runs produce a given outcome. This might help identify possible weather events, but doesn’t tell you real-world probabilities. If there is some factor that the computer model doesn’t take account of then running the computer model 50 times is in effect to make the same mistake 50 times.”

Let me elaborate.

We can dismiss the normal explanation for forecasting difficulties.  Forecasters normally plead “chaos”.  Perfect forecasts are impossible, they say, because the flap of a butterfly’s wings can cause a hurricane.  Small changes in initial conditions can have dramatic consequences.

I don’t accept this excuse for minute.

It may well be the case that computer models suffer badly from the chaos problem.  In fact, the ensemble modelling approach relies on it.  I suspect the real world is much less susceptible.  Besides, given enough computer power I could model the butterfly down to the last molecule and predict its wing-flapping in precise detail.

No, the real-world is determined. That is, there is only one possible outcome.  Given enough information and processing power you could, in principle, predict the future with complete accuracy.

Of course, there are insurmountable practical problems that prevent perfect forecasting:

• The most fundamental difficulty is that no computer can exceed the computing capabilities of the universe itself.  Although the future is written, it is in principle impossible to read it.
• You might try to get round the computing capacity problem by taking part of the universe as a closed system and building a huge computer to model what is going on in that relatively small part.  The difficulty then is that the entire universe is interconnected.  Every part of it is open, not closed.  If the small part you were modelling were the Earth, say, then you’d have to also model all celestial events, not just those which might have a physical effect, but all those which might be detectable by humans and therefore able to affect thought-processes and decision-making.  And, since our telescopes can see galaxies billions of light-years away, there’s a lot to include in your model.  That’s not all, though.  You’d also need to model every cosmic ray that might disrupt a molecule, most dramatically of germ-line DNA – though a change to any molecule is of consequence – and even every photon that might warm a specific electron, contribute to photosynthesis or allow a creature to see just that bit better when hunting…
• Then there are problems of what George Soros terms reflexivity.  That is, people’s behaviour is modified by knowing the predicted future.  They might act to deliberately avoid the modelled outcome, for example by deflecting an asteroid away from its path towards the Earth, which we might term strong reflexivity.  Or they might change their behaviour in a way that unintentionally affects the future, for example by cancelling travel plans in light of a weather forecast – weak reflexivity.  With enough computer power, some such problems could conceivably be overcome.  One might predict the response to an inbound asteroid, for example.  But it’s not immediately apparent how a model would handle the infinitely recursive nature of the general problem.

In practice, of course, these would be nice problems to have, because computer simulations of the weather system are grossly simplified.   They must therefore be systematically biased in their forecasting of any phenomena that rely on the complexity absent from the models.  As I noted yesterday, all runs in an ensemble forecast will suffer from any underlying bias in the model.

Two categories of simplification are problematic:

• Models divide the real-world into chunks, for example layers of the atmosphere (or of the ocean).
• And models necessarily represent closed systems – since the only truly closed system is the universe as a whole.  Anything not included in the model can affect the forecast.  For example, volcanic eruptions will invalidate any sufficiently long-term (and on occasion short-term) weather forecast.  Worse, weather models may be atmosphere only or include only a crude simplification of the oceans.  That is, they may represent the oceans in insufficient detail, and furthermore fail to include the effect of the forecast on the oceans, which in turn affects the forecast later on.

The good news, of course, is that it is possible to improve our weather forecasting almost indefinitely.

Perhaps those presenting weather forecasts should reflect on the fact that, as computer models improve, ensemble forecast ranges will narrow.  The 5-day forecast today is as good as the 3-day forecast was a decade or two ago. The probability of specific real-world conditions will not have changed.  That has always been and always will be precisely one: certainty.

It makes no sense to say “the probability of snow over Easter is x%”, when x depends merely on how big a computer you are using.

No, forecasters need to say instead that “x% of our forecasts predict snow over Easter”, which is not the same thing at all.

I’ll discuss communication problems more generally in a later post, but here I want to suggest the possibility that the outputs of forecasts – specifically ensemble forecasts – are being misinterpreted, and not just poorly communicated.

Anyone wanting an accessible introduction to the issues of forecasting, communicating forecasts and ensemble forecasting in particular, could do a lot worse than view the recent Royal Society debate, Storms, floods and droughts: predicting and reporting adverse weather. It’s entertaining too – there’s a great rant (with which I can’t help agreeing) from an audience member on the way the BBC reports London’s weather.

Ensemble forecasting is when a computer weather (or climate) model is run repeatedly – say 50 times – for the same forecast, but with very slightly different initial conditions (e.g. atmospheric pressure and temperature at particular locations). The idea is to produce a range of forecasts, representing the likelihood of possible outcomes. Tim Palmer suggests during the Royal Society debate that the most famous UK forecast ever – the dismissal in 1987 by Michael Fish of the possibility of a hurricane in Southern England the evening before one occurred – would instead have been presented probabilistically. Had he had an ensemble of forecasts, Fish might have said that there was a 30% probability of a hurricane.

I don’t agree with this.

If Fish had said there was a 30% probability of a hurricane he would have been guilty of confusing his computer model with reality.

All ensemble forecasters know is that a certain proportion of computer model runs produce a given outcome. This might help identify possible weather events, but doesn’t tell you real-world probabilities. If there is some factor that the computer model doesn’t take account of then running the computer model 50 times is in effect to make the same mistake 50 times.

March 2013 in the UK is the cold snap that just keeps on giving. The weather has defied forecasts. Specifically, it seemed just a few days ago that westerly air was going to break through before the end of March. Of course, this has a bearing on where March 2013 will rank among the all-time coldest, which I discussed in my previous post, but I’ll have to find time to revisit that subject in the next day or two.

The Weathercast site has made ensemble forecasts from the European Centre for Medium-range Weather Forecasts (ECMWF) available to the public. Here are some from over the last few days:

I’ve lined them up, so that the day the forecast is for appears in a column for forecasts as of 00:00 hours on 22nd, 24th and 25th March.

An ensemble that’s behaving itself should provide less of a spread of forecasts as we get closer to the forecast date. For example, the spread of the maximum temperature on Easter Day, 31st March narrows in the forecast from 25th March compared to that on 24th.

But now look at the coldest possible temperatures on 31st March. On 22nd hardly any predicted temperatures below 0C, and none below about -2C. By 25th most of the forecasts were for a frost on the morning of 31st, and many for a severe frost (-3C or so). This shouldn’t happen.

It seems that on 22nd nearly all the model runs predicted Atlantic air to break through by 31st; by 25th virtually none of them did.

Instead of fanning out more the longer in the future the forecast is for, the ensemble model outcome seems to change systematically. Perhaps ensemble forecasts don’t solve all our problems. I suspect there are aspects of the climate system our computer models do not yet capture. There are things we do not yet know.

As we saw for the unexpected rainfall in 2012, ensemble forecasts can predict zero probability of extreme events, in this case the (most likely) second coldest March since the 19th century. And the whole point of ensemble forecasts is to predict extremes.

The forecast for 31st March is of more than passing interest, of course. It is no doubt of great importance to those who may be planning to take school kids on Duke of Edinburgh expeditions on Dartmoor or (since we’re talking about a London forecast) preparing for a traditional Boat Race on the Thames!

This puzzled me a little since I noted only on Wednesday (and published only yesterday) that:

“…we have to go back to 1970 for the most recent March with an average CET of less than 4C, when 3.7C was recorded. It’s possible this March could even beat that mark.

But March 1969 was even colder at 3.3C. I doubt the figure for this year will come out below that. Most likely the headlines will be ‘coldest March for 44 years’.”

This passage is a little garbled because I only said it was “possible” this March could be colder than the 3.7C in March 1970 in the Central England Temperature (CET) record, yet implied that it would when I said it was “[m]ost likely” to be the “coldest March for 44 years”. I think I probably meant to write “for 43 years”, and could have added “with a possibility of it being the coldest March for 44 years”.

Over the last few days the forecast for the rest of the month has certainly turned decidedly wintry, as I discussed in my previous post, and even more so since I wrote, but is it now “certain” this March will be colder than in 1969?

CET vs UK Average Temperature: Comments on a BBC Assessment

A possible reason for my less bold temperature prediction is that the CET will turn out differently from the UK as a whole or for different regions. I’ve been assuming the CET is representative of the UK as a whole, but that might not always be the case.

In the absence of a contribution on the topic on the Met Office’s official blog, perhaps the BBC is the most authoritative source on weather statistics, being less inclined to hyperbole than most of the print media.

A post by John Hammond of the BBC suggests some slight differences between the UK figure and the CET. I assume Hammond is using the UK temperature because his figures are lower than the CET equivalents (and his figures tally with graphs available on the Met Office site – see below). He writes that:

“So far, March 2013 has been colder than both this winter’s December and January. The average temperature (day and night combined) for the UK this March to date is currently around 3C. It should normally be nearer 6C.”

The claim that March 2013 has “[s]o far” been colder than January is not true for the CET:

since January averaged 3.5C and so far March is 3.6C in the CET (rather than “around 3C”). The 3.6C figure for March was published in the last hour (as I type, rather than as I publish) – we’ll come back to the fact that the March figure has actually come down from 3.7C when Hammond was writing on Wednesday or Thursday.

Hammond goes on to say:

“…the coldest March on record was in 1962, when the mean temperature staggered to just 1.9C. That record will not be broken this year, but the more recent cold March of 1987 looks under threat – its mean temperature was 3.3C.”

not mentioning 1969 and 1970, for which the CET March temperatures fall between those in 1962 and 1987. This is a little odd since the same is true for the UK as a whole, which is what Hammond’s data seems to relate to. To admit my ignorance, I don’t know how to access the actual UK figures (maybe I should ask the Met Office), but I do know how to plot them graphically from a handy Met Office page:

Note the cold Marches in 1969 and 1970, which Hammond doesn’t remark on. Maybe that’s an oversight.

So, will it be colder this March than in 1969?

Since the media are so sure March 2013 will be the coldest “for 50 years” (meaning 51), let’s have another look.

The first point to note is that the average so far this month, up to and including the 21st, is 3.6C. As I mentioned, it was only 3.7C to the 19th and the 20th. In terms of record-breaking, this could be enough to make a difference.

The second point is arithmetical. If one of the remaining 10 days this month (22nd-31st) is 2-3C below the current average (3.6C), the mean for the month will decrease by 0.1C; if a day is 2-3C above the average so far the mean will increase by 0.1C. This is admittedly a crude reckoning system, but simple and effective.

Third, taking the Heathrow temperature as typical of the Central England region as a whole, the medium term forecast has been deteriorating. This was the main theme of my previous post – perhaps I didn’t take enough account of it when discussing the monthly record temperatures.

This is what the forecasts looked like a couple of days ago (thanks Weathercast):

and this is the latest graph:

The forecasts do seem to have deteriorated even further than I discussed in my previous post.

Ignoring today (22nd) as transitional, it now looks likely that the 5 days 23rd through 27th March will be seriously cold, so let’s knock 0.1C off the monthly average for each of them. That gets us down to 3.1C.

The 28th will most likely be around the new average (3.1C), so it all depends on when the mild air comes in from the Atlantic. The computer model runs (grey lines) differ, and the average (yellow line) for 30th and 31st are for it to be relatively mild. If that’s the case, then we’d need to add on 0.1C for each day, so would roughly equal 1969.

The grey lines represent an ensemble of forecasts, I assume each less precise than those generating the published maps. If we go on the basis of the main model runs (the red and blue lines), of which the ECMWF (red line) seems to me to have been best at predicting the “battle” between cold easterly and mild westerly air this winter (as in fact exemplified by the pair of Weathercast graphs above), then it looks fairly cold through almost to the end of the month.

The balance of probabilities does seem now to suggest that March 2013 will be the coldest in the CET since 1962. Most likely, the Metro, the Mail and John Hammond of the BBC will be proved right.

It might be worth noting that if the CET this month is lower than not just 3.3C, but the 3.2C recorded in both 1917 and 1955, it will not only be the coldest March in the series since 1962, but the second coldest since the 19th century. This is where the CET is useful – it gives a longer historical perspective than the UK figures, which only go back to 1910.

I suppose it’s not outside the bounds of possibility that we’ll beat that 1962 figure of a March CET of 2.8C, but that remains very unlikely.

All this may seem nit-picking, but if we’re going to make claims about increased frequency of weather extremes – and policy based on those claims – it’s essential to be clear what the data is telling us.

I checked the weather forecast, as I normally do, and was amazed to discover that the temperatures later in the week (i.e. for Friday 22nd and Saturday 23rd) were predicted to be fully 5C colder than I’d remembered they’d forecast just the previous day! Yet more snow is now expected over much of the country.

The result is that March 2013 is now likely to be the coldest for fully 40 years.

I’ll cover the forecasting difficulties first – a side-issue really, but notable, nonetheless – and then look at how cold this March has been.

A Knife-Edge Winter Forecast

Luckily, when I switched on my work computer this morning (Wednesday 20th) the forecasts made by the Met Office on 19th were still cached by Firefox, so I was able to do some screen-grabs. Here’s the one for the weather at Heathrow on Friday 22nd, as of 11:00 Tuesday 19th:

when they were expecting the temperature to reach 9C in the afternoon.

By 10:00 on Wednesday 20th, though, they were forecasting a peak temperature of only 4C on Friday:

Similarly the forecast for Saturday as of Tuesday morning was for 9C:

and 4C as of Wednesday morning:

Furthermore, a notably cold forecast for Sunday was available on Wednesday:

Curiously, as I complete this post on Thursday, I see that the forecast is now for even colder weather on Sunday. This is worth including as the London temperature is expected to be around the same as on 11th, which was billed as the coldest March day for almost 30 years (since 1st March 1986, just after that record-breaking bitter February I might have mentioned before) for the country as a whole:

Why this sudden change in the forecast?

The answer is the difficulty in predicting the outcome of what is often termed the “battle” over the UK between cold easterlies and mild westerlies. The following charts show an an Atlantic weather system pushing in, bringing the rain seen in the forecasts above for Friday in particular. On Tuesday the system was expected to move across much of the country:

I’ve indicated the warm front, behind which the air is milder with a red arrow and the cold air with a blue arrow.

The weather map published on Wednesday was subtly different:

At first glance it seems little has changed, but in fact the warm front (red arrow) has pushed much less further north and east.

For completeness we see that the front, now indicated with a green arrow because it is occluded (hey, I’ve got a colour palette and I’m going to use it), is expected to be stuck over the country by Saturday:

So what seems a minor detail in the great scheme of things has a significant effect on the weather in one particular place, in this case much of the UK. Quite a bit of snow is now expected, though not in London, alas.

Clearly the Met Office need even bigger computers! They were big enough to ‘fess up in their weather-warning:

March 2013 in the CET

The difference between forecasts on Tuesday and on Wednesday is sufficient to change the predicted temperature for the whole of March. As in previous posts, most recently for this winter up to February, I prefer to look at the Central England Temperature (CET) series, because it gives a decent historical perspective.

Here’s the monthly data for the last few years, courtesy of the Met Office:

The temperature so far for March is 3.7C. With cold weather expected until at least 28th, it is unlikely that the mean temperature in the CET will exceed 4C for the month as a whole. This will make it the coldest March for over 40 years. For once it seems the media have understated rather than exaggerated (though maybe measures other than the CET are turning out differently).

It looks almost certain we’ll beat March 2006 at 4.9C, and extremely likely the 4.5C in March 1996 will not be exceeded.

Curiously March 1996 and March 2006 are the only Marches (apart from 2013) averaging less than 5C since a run of 4 from 1984-7. One wonders if it is more than coincidence that this run followed the El Chichon eruption in 1982. Anyway, the coldest March of the 1980s was 1987 at 4.1C. It seems likely we’ll be colder than that this year as well.

Marches colder than 5C seem to have been more frequent back in the day, occurring in 1971, 1975, 1976, 1979 and 1980. Many would attribute the much reduced frequency in the 1990s, 2000s and so far in the 2010s to global warming, making this year even more exceptional (like the summer of 2011).

But we have to go back to 1970 for the most recent March with an average CET of less than 4C, when 3.7C was recorded. It’s possible this March could even beat that mark.

But March 1969 was even colder at 3.3C. I doubt the figure for this year will come out below that. Most likely the headlines will be “coldest March for 44 years”.

For the record, March 1962 was even colder at 2.8C, there was a 2.7C in 1892 and 1.9C in 1883. The record seems to be 1.2C in 1785, though really we should discount those clearly influenced by eruptions, in that case Laki, which must surely explain the run of 4 cold Marches from 1783: 3.3C that year, through 2.7C in 1784, 1.2C in 1785, as mentioned, to 2.1C in 1786. Of course, it was generally colder in that period as well.

March 2013 has been so cold that I thought I’d produce one of my CET graphs for the “long winter”, that is December to March inclusive:

In general including March makes surprisingly little difference (compare the similar chart for December through February in my last weather post). The longer perspective makes winter 2012-13 closer in coldness to 2009-10, but it’s still not historically very significant. Further back, 1962-3 becomes less notable, struggling to hold on to 4th place in the all-time coldest winter stakes, rather than challenging for 2nd, with 1813-14, famous for the last Frost Fair on the Thames, colder on a 4 month comparison. 1683-4 remains the outlier.

The running means (green, red and black lines) show that our “long winters” are not yet as cold as around 1980, which was milder than in the early 1960s, which in turn was less cold than in the late 19th century and the mid 18th. The late 17th century was colder still. The late 20th century and early 21st century mildness is attributable to global warming, of course.

CET Anomaly Annual Running Mean Goes Negative

What seems most significant about this March to me, though, is that it completes a run of 12 months colder in the CET than the 1961-90 mean.

I provided the monthly data to date for this year and for the 3 previous years earlier in the post. You can see that 2012 was only 0.2C warmer than the historical average. The first 3 months this year will have been significantly colder than in 2012, especially March which will be colder by more than 4C, maybe approaching 5C! The result is that the average of April 2012 through March 2013 is well below the 1961-90 figure (just average the anomaly column). (Sorry, no time just now to produce a CET 12 month running mean graph – another time maybe).

2010 was also significantly (0.6C) colder than the long-term average, as a result of the record-breaking December and, to a lesser extent, the cold January that year.

There were, previous to 2010, some 13 years of temperatures above the 1961-90 mean:

Since the global temperature data annual mean shows temperatures remaining as high in the 2010s as in the 1990s and 2000s, it does rather seem as if a change in weather patterns is now counteracting some of the effect of global warming on UK temperatures apparent through the two decades of the 1990s and 2000s.

Finally, it’s now looking unlikely that the year 2013 as a whole will approach the mean temperature seen in many of those years in the 1990s and 2000s. Then again, 2011 had a very mild summer, yet, taken as whole, wasn’t far off the warmest year on record. My understanding is that, because of global warming, we’re tending to get exceptionally warm months, such as February, April and November 2011, far more frequently than in the past. I expect we’ll see one again soon, though I have a hunch the next time the weather is notable enough for me to put together a blog post, it’ll be flooding I’m taking about, again.